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1.
We show the nonvanishing of H
0(X,−K
X
) for any a Fano 3-fold X for which −K
X
is a multiple of another Weil divisor in Cl(X). The main case we study is Fano 3-folds with Fano index 2: that is, 3-folds X with rank Pic(X)=1, -factorial terminal singularities and −K
X
= 2A for an ample Weil divisor A. We give a first classification of all possible Hilbert series of such polarised varieties (X,A) and deduce both the nonvanishing of H
0(X,−K
X
) and the sharp bound (−K
X
)3≥ 8/165. We find the families that can be realised in codimension up to 4. 相似文献
2.
Yuefei Wang 《Archiv der Mathematik》1997,68(4):300-310
The complex oscillation of nonhomogeneous linear differential equations with transcendental coefficients is discussed. Results
concerning the equation f
(k)+a
k−1
f
(k−1)+...+a
0
f=F where a
0,...,a
k−i and Fare entire functions, possessing an oscillatory solution subspace in which all solutions (with at most one exception)
have infinite exponent of convergence of zeros are obtained. All solutions of the equation are also characterized when the
coefficients a
0,a
1,...,a
k−1 are polynomials and F=h exp (p
0), where p
0 is a polynomial and h is an entire function.
Author supported by Max-Planck-Gesellschaft and by NSFC. 相似文献
3.
4.
Optimal in a certain sense sufficient conditions are given for the existence and uniqueness of ω-periodic solutions of the
nonautonomous ordinary differential equation u
(2m)
=f(t,u,...,u
(m-1)
), where the function f:ℝ×ℝ
m
→ℝ is periodic with respect to the first argument with period ω.
Received: December 21, 1999; in final form: August 12, 2000?Published online: October 2, 2001 相似文献
5.
LetK be a number field. Denote byV
3 a split Del Pezzo surface of degree six overK and by ω its canonical divisor. Denote byW
3 the open complement of the exceptional lines inV
3. LetN
W
s(−ω, X) be the number ofK-rational points onW
3 whose anticanonical heightH
−ω is bounded byX. Manin has conjectured that asymptoticallyN
W
3(−ω, X) tends tocX(logX)3, wherec is a constant depending only on the number field and on the normalization of the height. Our goal is to prove the following
theorem: For each number fieldK there exists a constantc
K such thatN
W
3(−ω, X)≤cKX(logX)3+2r
, wherer is the rank of the group of units ofO
K. The constantc
K is far from being optimal. However, ifK is a purely imaginary quadratic field, this proves an upper bound with a correct power of logX. The proof of Manin's conjecture for arbitrary number fields and a precise treatment of the constants would require a more
sophisticated setting, like the one used by [Peyre] to prove Manin's conjecture and to compute the correct asymptotic constant
(in some normalization) in the caseK=ℚ. Up to now the best result for arbitraryK goes back, as far as we know, to [Manin-Tschinkel], who gives an upper boundN
W
3(−ω,X)≤cXl+ε.
The author would like to express his gratitude to Daniel Coray and Per Salberger for their generous and indispensable support. 相似文献
6.
The singular integral operator J Ω,α, and the Marcinkiewicz integral operator (~μ)Ω,α are studied. The kernels of the operators behave like |y|-n-α(α>0) near the origin, and contain an oscillating factor ei|y|-β(β>0) and a distribution Ω on the unit sphere Sn-1 It is proved that, if Ω is in the Hardy space Hr (Sn-1) with 0<r= (n-1)/(n-1 )(>0), and satisfies certain cancellation condition,then J Ω,α and uΩ,α extend the bounded operator from Sobolev space Lpγ to Lebesgue space Lp for some p. The result improves and extends some known results. 相似文献
7.
In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L
2(ℝ
s
). Suppose ψ = (ψ1,..., ψ
r
)
T
and are two compactly supported vectors of functions in the Sobolev space (H
μ(ℝ
s
))
r
for some μ > 0. We provide a characterization for the sequences {ψ
jk
l
: l = 1,...,r, j ε ℤ, k ε ℤ
s
} and to form two Riesz sequences for L
2(ℝ
s
), where ψ
jk
l
= m
j/2ψ
l
(M
j
·−k) and , M is an s × s integer matrix such that lim
n→∞
M
−n
= 0 and m = |detM|. Furthermore, let ϕ = (ϕ1,...,ϕ
r
)
T
and be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, and M, where a and are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr
)
T
and , ν = 1,..., m − 1 such that two sequences {ψ
jk
νl
: ν = 1,..., m − 1, l = 1,...,r, j ε ℤ, k ε ℤ
s
} and { : ν=1,...,m−1,ℓ=1,...,r, j ∈ ℤ, k ∈ ℤ
s
} form two Riesz multiwavelet bases for L
2(ℝ
s
). The bracket product [f, g] of two vectors of functions f, g in (L
2(ℝ
s
))
r
is an indispensable tool for our characterization.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10771190, 10471123) 相似文献
8.
Following [5], aT
3 spaceX is called good (splendid) if it is countably compact, locally countable (andω-fair).G(κ) (resp.S(κ)) denotes the statement that a good (resp. splendid) spaceX with |X|=κ exists. We prove here that (i) Con(ZF)→Con(ZFC+MA+2
ω
is big+S(κ) holds unlessω=cf(κ)<κ); (ii) a supercompact cardinal implies Con(ZFC+MA+2suω>ω+1+┐G(ωω+1); (iii) the “Chang conjecture” (ωω+1),→(ω
1,ω) implies ┐S(κ) for allκ≧k≧ωω; (iv) ifP addsω
1 dominating reals toV iteratively then, in
, we haveG(λω) for allλ.
Research supported by Hungarian National Foundation for Scientific Research grant no. 1805. 相似文献
9.
Let I≥1 be an integer, ω
0=0<ω
1<⋯<ω
I
≤π, and for j=0,…,I, a
j
∈ℂ, a-j=[`(aj)]a_{-j}={\overline{{a_{j}}}}, ω
−j
=−ω
j
, and aj 1 0a_{j}\not=0 if j 1 0j\not=0. We consider the following problem: Given finitely many noisy samples of an exponential sum of the form
[(x)\tilde](k) = ?j=-II ajexp(-iwjk) +e(k), k=-2N,?,2N,\tilde{x}(k)= \sum_{j=-I}^I a_j\exp(-i\omega _jk) +\epsilon (k), \quad k=-2N,\ldots,2N, 相似文献
10.
Here we prove the following result.
Theorem 1.1.Let X be an integral projective curve of arithmetic genus g and k≧ ≧4 an integer. Assume the existence of L ∈ Pick
(X) with h
0
(X, L)=2 and L spanned. Fix a rank 1 torsion free sheaf M on X with h
0(X,M)=r+1≧2, h1
(X, M)≧2 and M spanned by its global sections. Set d≔deg(M) and s≔max {n≧0:h
0 (X, M ⊗(L*)⊗n)>0}. Then one of the following cases occur:
Sunto In questo lavoro si dimostra il seguente teorema. Teorem 1.1.Sia X una curva proiettiva ridotta e irriducibile di genere aritmetico g e k≥4 un intero. Si supponga l'esistenza di L ε Pick (X) con h 0 (X, L)=2 e L generato. Si fissi un fascio senza torsione di rango uno M su X con h0 (X, M)=r++1≥2, h1 (X, M) ≧2 e M generato dalle sue sezioni globali. Si ponga d≔deg(M) e s≔max{n≧0:h 0(X, M ⊗(L*)⊗n)>0}. Allora si verifica uno dei casi seguenti:相似文献 11.
Guoxiang Chen Meiying Wang 《分析论及其应用》2007,23(3):266-273
For a continuous, increasing function ω: R → R \{0} of finite exponential type, this paper introduces the set Z(A, ω) of all x in a Banach space X for which the second order abstract differential equation (2) has a mild solution such that [ω(t)]-1u(t,x) is uniformly continues on R , and show that Z(A, ω) is a maximal Banach subspace continuously embedded in X, where A ∈ B(X) is closed. Moreover, A|z(A,ω) generates an O(ω(t))strongly continuous cosine operator function family. 相似文献
12.
Dr. Lionel Weiss 《Probability Theory and Related Fields》1968,10(3):193-197
Summary
X
1,...,X
n
are independent random variables, identically distributed over the unit interval, with common probability density function 1 + r(x)/n
for all sufficiently large n, where is a positive constant,
and |r(x)| <D. V
1, ..., V
n+1 are the sample spacings generated by X
1,..., X
n
. It is shown that in many cases, the asymptotic joint distribution of homogeneous functions of V
1,..., V
n+1 can be found directly from the asymptotic joint distribution of homogeneous functions of independent exponential random variables.Research supported by NSF Grant GP 3783. 相似文献
13.
Dieter Bothe 《Israel Journal of Mathematics》1998,108(1):109-138
Given anm-accretive operatorA in a Banach spaceX and an upper semicontinuous multivalued mapF: [0,a]×X→2
X
, we consider the initial value problemu′∈−Au+F(t,u) on [0,a],u(0)=x
0. We concentrate on the case when the semigroup generated by—A is only equicontinuous and obtain existence of integral solutions if, in particular,X* is uniformly convex andF satisfies β(F(t,B))≤k(t)β(B) for all boundedB⊂X wherek∈L
1([0,a]) and β denotes the Hausdorff-measure of noncompactness. Moreover, we show that the set of all solutions is a compactR
δ-set in this situation. In general, the extra condition onX* is essential as we show by an example in whichX is not uniformly smooth and the set of all solutions is not compact, but it can be omited ifA is single-valued and continuous or—A generates aC
o-semigroup of bounded linear operators. In the simpler case when—A generates a compact semigroup, we give a short proof of existence of solutions, again ifX* is uniformly (or strictly) convex. In this situation we also provide a counter-example in ℝ4 in which no integral solution exists.
The author gratefully acknowledges financial support by DAAD within the scope of the French-German project PROCOPE. 相似文献
14.
Hari Bercovici 《Complex Analysis and Operator Theory》2007,1(3):335-339
Consider a domain
, and two analytic matrix-valued functions functions
. Consider also points
and positive integers n
1, n
2, . . . , n
N
. We are interested in the existence of an analytic function
such that X(ω) is invertible, and G(ω) coincides with X(ω)F(ω)X(ω)−1 up to order n
j
at the point ω
j
. We will see that such a function exists provided that F(ω
j
),G(ω
j
) have cyclic vectors, and the characteristic polynomials of F,G coincide up to order n
j
at ω
j
. This allows one to give a short proof to a result of Huang, Marcantognini and Young concerning spectral interpolation in
the unit disk.
The author was partially supported by a grant from the National Science Foundation.
Received: September 8, 2006. Accepted: January 11, 2007. 相似文献
15.
Qualitative and spectral properties of the form sums
16.
Summary. We address the following problem from the intersection of dynamical systems and stochastic analysis: Two SDE dx
t
= ∑
j
=0
m
f
j
(x
t
)∘dW
t
j
and dx
t
=∑
j
=0
m
g
j
(x
t
)∘dW
t
j
in ℝ
d
with smooth coefficients satisfying f
j
(0)=g
j
(0)=0 are said to be smoothly equivalent if there is a smooth random diffeomorphism (coordinate transformation) h(ω) with h(ω,0)=0 and Dh(ω,0)=id which conjugates the corresponding local flows,
17.
Christian Wegner 《manuscripta mathematica》2009,128(4):469-481
Let X be a finite aspherical CW-complex whose fundamental group π
1(X) possesses a subnormal series with a non-trivial elementary amenable group G
0. We investigate the L
2-invariants of the universal covering of such a CW-complex X. The main result is the proof of the vanishing of the L
2-torsion under the condition that π
1(X) has semi-integral determinant. We further show that the Novikov–Shubin invariants are positive. 相似文献
18.
Giuliano Mazzanti 《Annali dell'Universita di Ferrara》1972,17(1):143-147
Riassunto Si dà la definizione di classe ?localmente filtrale?. Si diceche K è una classe localmente filtrale se per ogni n∈ω, per ogni
A
0,...,A
n−1, εK e per ogni famiglia di sotto-insiemi Vi di Ai (i∈n) con Vi finiti, la classe {B
0,...,B
n−1 delle algebre generate da V0, ..., Vn−1 è costituita da algebre finite ed è filtrale.
Si dimostra che seK è localmente filtrale alloraV
L(K)=IR
L
DS(K) e si dà un teorema di caratterizzazione per queste classi.
Summary We define a ?classe localmente filtrale? as follows: LetK be a class of similar algebras;K is a ?classe localmente filtrale? if for andn ∈ ω and for anyA 0,...,A n−1 ink and for any family of finite subsetsV i ofA i(i∈n), the class {B 0,...,B n−1 of algebras generated byV o, ...,V n−1 consists of finite algebras and is ?filtrale?. We show that ifK is ?localmente filtrale? thenV L (K)=IR L DS(K) and we give a characterization theorem for these classes. Lavoro eseguito nell'ambito dei gruppi di ricerca matematici del C.N.R. per l'anno 1970–71. 相似文献 19.
Abdoulaye Guiro 《Annali dell'Universita di Ferrara》1994,40(1):1-21
Resume Le principail résultat de ce travail est un Théorème d’approximation des sections différentiables d’un fibré linéaireF sur un espace analytique réel cohérentX. (I) On définit le concept de sections différentiables d’un tel fibré puis le faisceau des germes de sections différentiablesC
∞ (F) qui s’identifie àF
∞=F⊗
Ox
C
X
∞
:F=dual du fibré linéaireF,C
X
∞
=faisceau des germes de fonctions différentiables surX. (II)X est supposé en plus paracompact et localement compact. On construit surF
∞(X) une ?topologie de Whitney? pour laquelleF(X) est dense dansF
∞(X). La démonstration utilise les complexifiés
et
et les voisinages de Stein deX dans
.
Sunto Il risultato principale di questo lavoro è un teorema di approssimazione delle sezioni differenziabili di un fibrato lineareF su uno spazio analitico reale coerenteX. (I) Si definisce il concetto di sezione differenziabile di un tale fibrato poi il fascio dei germi delle sezioni differenziabiliC ∞ (F) che si identifica aF ∞=F⊗ Ox C X ∞ :F=duale del fibrato lineareF,C X ∞ dei germi delle funzioni differenziabili suX. (II)X è supposto inoltre paracompatto e localmente compatto. Si costruisce suF ∞ (X) una ?topologia di Whitney? per la qualeF(X è denso inF ∞(X). La dimostrazione utilizza i complessificati e e gli intomi di Stein diX in .相似文献 |